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Sep 21, 2013
09/13

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Eric Braaten; H. -W. Hammer

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The two-body scattering length a for 4He atoms is much larger than their effective range r_s. As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by r_s/a, all low-energy three-body observables are determined by a and a three-body parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for the trimer binding energy equation, the atom-dimer...

Source: http://arxiv.org/abs/cond-mat/0203421v2

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Sep 19, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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Efimov physics refers to universal phenomena associated with a discrete scaling symmetry in the 3-body problem with a large scattering length. The first experimental evidence for Efimov physics was the recent observation of a resonant peak in the 3-body recombination rate for 133Cs atoms with large negative scattering length. There can also be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We calculate the atom-dimer relaxation rate as a function of...

Source: http://arxiv.org/abs/cond-mat/0610116v2

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Sep 22, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature....

Source: http://arxiv.org/abs/1302.5617v2

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Sep 20, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. In the 3-body sector for identical bosons, the universal properties include the existence of a sequence of shallow 3-body bound states called "Efimov states" and log-periodic...

Source: http://arxiv.org/abs/cond-mat/0410417v3

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Sep 19, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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Small increases in the up and down quark masses of QCD would tune the theory to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At critical values of the quark masses, the deuteron binding energy goes to zero and the triton has infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states approaches a universal constant that is close to 515. The proximity of...

Source: http://arxiv.org/abs/nucl-th/0303038v1

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Sep 24, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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An effective field theory for the three-body system with large scattering length a is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant \alpha is calculated to first order in the short-distance interactions that allow the recombination. For a < 0, the dimensionless combination m \alpha/(\hbar a^4) is a periodic function of \ln |a| that exhibits resonances at values of a that differ by multiplicative factors of 22.7. This dramatic behavior...

Source: http://arxiv.org/abs/cond-mat/0103331v2

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Sep 20, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and...

Source: http://arxiv.org/abs/cond-mat/0612123v1

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Sep 22, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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We conjecture that QCD can be tuned to an infrared limit cycle in the three-nucleon system by adjusting the up and down quark masses to critical values at which the binding energies of the deuteron and its spin-singlet partner are tuned to zero. At the critical point, the triton would have infinitely many arbitrarily-shallow excited states with the ratio of the binding energies of successive states approaching a universal constant close to 515.

Source: http://arxiv.org/abs/nucl-th/0309030v2

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Sep 23, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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The dark matter annihilation rate at small relative velocities can be amplified by a large boost factor using various mechanisms, including Sommerfeld enhancement, resonance enhancement, and Breit-Wigner enhancement. These mechanisms all involve a resonance near the threshold for a pair of dark matter particles. We point out that if the resonance is in the S-wave channel, the mechanisms are equivalent sufficiently near the resonance and they are constrained by universal two-body physics. The...

Source: http://arxiv.org/abs/1303.4682v2

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Sep 18, 2013
09/13

by
Eric Braaten; H. -W. Hammer

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We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that...

Source: http://arxiv.org/abs/cond-mat/0303249v2

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Jul 19, 2013
07/13

by
Eric Braaten; H. -W. Hammer; Thomas Mehen

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The identification of the X(3872) as a loosely-bound charm-meson molecule allows it to be described by an effective field theory, called XEFT, for the D^* Dbar, D Dbar^* and D Dbar pi sector of QCD at energies small compared to the pion mass. We point out that this effective field theory can be extended to the sector that includes an additional pion and used to calculate cross sections for the scattering of a pion and the X(3872). If the collision energy is much smaller than the pion mass, the...

Source: http://arxiv.org/abs/1005.1688v1

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Sep 19, 2013
09/13

by
Eric Braaten; H. -W. Hammer; M. Kusunoki

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Recent experiments with Bose-Einstein condensates of 85Rb atoms near a Feshbach resonance have produced evidence for a condensate of diatomic molecules coexisting with the atom condensate. It should also be possible to create condensates of the triatomic molecules predicted by Efimov coexisting with the atom and dimer condensates. The smoking gun for the trimer condensate would be oscillatory dependence of observables on the binding energy of the trimer. It may also be possible to deduce the...

Source: http://arxiv.org/abs/cond-mat/0206232v3

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Sep 20, 2013
09/13

by
Eric Braaten; H. -W. Hammer; M. Kusunoki

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In Phys. Rev. Lett. 89, 180401 (2002) [cond-mat/0204504], Kokkelmans and Holland interpret the results of a recent experiment at JILA that demonstrated atom-molecule coherence in a Bose-Einstein condensate. Using a mean-field approximation to a resonance field theory involving an atom condensate and a molecular condensate, they find that the molecular condensate is tiny compared to the atom condensate. We show that if the probability for the molecular field to create a diatomic molecule is...

Source: http://arxiv.org/abs/cond-mat/0301489v1

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Sep 17, 2013
09/13

by
Eric Braaten; H. -W. Hammer; Thomas Mehen

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We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density of the homogeneous Bose-Einstein condensate to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda_* that determines the low-energy observables in the 3-body sector. The second-order correction to the energy density has a small imaginary part that reflects the instability due to 3-body recombination....

Source: http://arxiv.org/abs/cond-mat/0108380v2

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Sep 18, 2013
09/13

by
Eric Braaten; H. -W. Hammer; Shawn Hermans

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Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact...

Source: http://arxiv.org/abs/cond-mat/0012043v1

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Sep 22, 2013
09/13

by
Eric Braaten; H. -W. Hammer; M. Kusunoki

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Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He atoms. We also extend Efimov's theory to include...

Source: http://arxiv.org/abs/cond-mat/0201281v3

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Jun 29, 2018
06/18

by
Eric Braaten; Hans-Werner Hammer; G. Peter Lepage

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The loss of particles due to highly inelastic reactions has previously been taken into account in effective field theories for low-energy particles by adding local anti-Hermitian terms to the effective Hamiltonian. An additional modification is required in the time evolution equation for the density matrix of a multi-particle system. An effective density matrix can be defined by tracing over states containing high-momentum particles produced by the highly inelastic reactions and by a time...

Topic: High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1612.08047

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Jun 29, 2018
06/18

by
Eric Braaten; H. -W. Hammer; G. Peter Lepage

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Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-particle systems are considered, an additional modification is required in equations governing the density matrix. We...

Topics: High Energy Physics - Theory, High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1607.02939

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Sep 22, 2013
09/13

by
Eric Braaten; H. -W. Hammer; Daekyoung Kang; Lucas Platter

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The 3-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex valued. We provide semi-analytic expressions for the cases of 2 or 3 equal scattering lengths and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three...

Source: http://arxiv.org/abs/0811.3578v2

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Sep 23, 2013
09/13

by
Eric Braaten; P. Hagen; H. -W. Hammer; L. Platter

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Resonant P-wave interactions can be described by a minimal zero-range model defined by a truncated effective range expansion, so that the only 2-body interaction parameters are the inverse scattering volume 1/a_P and the P-wave effective range r_P. This minimal model can be formulated as a local quantum field theory with a P-wave interaction between atom fields and a molecular field. In the two-atom sector, the model is renormalizable, but it has unphysical behavior at high energies, because...

Source: http://arxiv.org/abs/1110.6829v4

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Jun 29, 2018
06/18

by
Eric Braaten; H. -W. Hammer; G. Peter Lepage

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The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic...

Topics: High Energy Physics - Phenomenology, Condensed Matter, Quantum Gases

Source: http://arxiv.org/abs/1607.08084

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Sep 22, 2013
09/13

by
Eric Braaten; H. -W. Hammer; Daekyoung Kang; Lucas Platter

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A new narrow 3-atom loss resonance associated with an Efimov trimer crossing the 3-atom threshold has recently been discovered in a many-body system of ultracold 6Li atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O'Hara and coworkers have used measurements of the 3-body recombination rate in this region to determine the complex 3-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the...

Source: http://arxiv.org/abs/0908.4046v2

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Sep 23, 2013
09/13

by
Eric Braaten; H. -W. Hammer; Daekyoung Kang; Lucas Platter

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For identical bosons with a large scattering length, the dependence of the 3-body recombination rate on the collision energy is determined in the zero-range limit by universal functions of a single scaling variable. There are six scaling functions for angular momentum zero and one scaling function for each higher partial wave. We calculate these universal functions by solving the Skorniakov--Ter-Martirosian equation. The results for the 3-body recombination as a function of the collision energy...

Source: http://arxiv.org/abs/0801.1732v2